Question

PLEASE ANSWER ASAP WILL MARK BRAINLIEST solve for x write both solutions. 6x^2-7x-3=0

Answer 1

$6x^2-7x-3=0\\\\6x^2-9x+2x-3=0\\\\3x(2x-3)+1(2x-3)=0\\\\(2x-3)(3x+1)=0\iff2x-3=0\ \vee\ 3x+1=0\\\\2x-3=0\ \ \ |+3\\2x=3\ \ \ |:2\\x=\dfrac{3}{2}\\\\3x+1=0\ \ \ |-1\\3x=-1\ \ \ |:3\\x=-\dfrac{1}{3}$

$Answer:\ \boxed{x=-\dfrac{1}{3}\ \vee\ x=\dfrac{3}{2}}$

Answer 2

6x^2-7x-3=0
Solve by completing the square:
x^2-7/6x-1/2=0 (divided everything by 6)
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of bb, the coefficient of x.(b/2)2=(−7/12)2
x2−7x/6+(−7/12)2=1/2+(−7/12)2
(simplify)
x2−7x6+49144=121144x2-7x6+49144=121144Factor the perfect trinomial square into (x−7/12)2(x−7/12)2=121/144
x-7/12=squ. root of +/- 121/144
x-7/12= +/- 11/12
Solution1:
x-7/12=11/12
x=18/12
x=3/2
Solution 2:
x-7/12=-11/12
x=-4/12
x=-1/3
Answers: 3/2, -1/3